Optimal Risk-Sharing Across a Network of Insurance Companies

Insurance: Mathematics and Economics, 95, 39-47 (2020)

Swiss Finance Institute Research Paper No. 20-52

23 Pages Posted: 29 Jun 2020 Last revised: 9 Sep 2020

See all articles by Nicolas Ettlin

Nicolas Ettlin

University of Basel, Actuarial Science, Department of Mathematics and Computer Science

Walter Farkas

University of Zurich - Department of Banking and Finance; Swiss Finance Institute; ETH Zürich

Andreas Kull

University of Basel, Actuarial Science, Department of Mathematics and Computer Science; BerninaRe Ltd.

Alexander Smirnow

University of Zurich - Department of Banking and Finance

Date Written: June 19, 2020

Abstract

Risk transfer is a key risk and capital management tool for insurance companies. Transferring risk between insurers is used to mitigate risk and manage capital re- quirements. We investigate risk transfer in the context of a network environment of insurers and consider capital costs and capital constraints at the level of individual insurance companies. We demonstrate that the optimisation of profitability across the network can be achieved through risk transfer. Considering only individual in- surance companies, there is no unique optimal solution and, a priori, it is not clear which solutions are fair. However, from a network perspective, we derive a unique fair solution in the sense of cooperative game theory. Implications for systemic risk are briefly discussed.

Keywords: risk transfer, risk-based capital, reinsurance, return optimisation, conditional expected shortfall

JEL Classification: G13, G22, D85, C57, C71

Suggested Citation

Ettlin, Nicolas and Farkas, Walter and Kull, Andreas and Kull, Andreas and Smirnow, Alexander, Optimal Risk-Sharing Across a Network of Insurance Companies (June 19, 2020). Insurance: Mathematics and Economics, 95, 39-47 (2020), Swiss Finance Institute Research Paper No. 20-52, Available at SSRN: https://ssrn.com/abstract=3417016 or http://dx.doi.org/10.2139/ssrn.3417016

Nicolas Ettlin

University of Basel, Actuarial Science, Department of Mathematics and Computer Science ( email )

Petersplatz 1
Basel, CH-4003
Switzerland

Walter Farkas

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland
+41-44-634 3953 (Phone)
+41-44-634 4345 (Fax)

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

Andreas Kull

University of Basel, Actuarial Science, Department of Mathematics and Computer Science ( email )

Petersplatz 1
Basel, CH-4003
Switzerland

BerninaRe Ltd. ( email )

Victoria Place
31 Victoria Street
Hamilton, HM1
Bermuda

Alexander Smirnow (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland

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